Partial keyless entry fix

The "new" '92 LS400 we picked up had a non-functioning keyless entry system. I checked the usual DOME fuse but it was fine. After pulling the key fob apart, I found a cold solder joint on what I think is the link to the antenna/transmitter part of the key fob. While disassembly the fob, I gently pried the circuit board up and noticed the wire was moving inside the solder joint. You can see the part that I reflowed the solder on in red here:

Now the keyfob works, but the range is *very* short. It's 50/50 that it'll work if I stand right next to the car, doesn't work at all from ten feet away, but works 100% if I touch the key to something like the metal antenna on the car. The battery in the key fob tests out at 3V DC as it should. What kind of range should this thing work at? Would it be worth pulling the keyless entry ECU in the trunk out and giving the contacts a good cleaning? Does that ECU have it's own antenna or is it connected to the car antenna?

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My keyless on my 91 is iffy. It only works in one of the two keys I have, and the range is maybe 5-7 feet. Sometimes it will be a douchebag and just not go, and won't lock until I walk to the other side of the car but that rarely happens.